I already understand how to balance a redox reaction, considering the environment in which they occur. However, I do not understand why do we need to consider that. I mean, why do OH- and H20 and H+ interfere with the reactions?

What you need to remember is that a redox reaction involves the transfer of electrons from one species to another. If one of the species losses two electrons, then something else needs to accept two electrons. The electrons have to go somewhere; that is what you are actually balancing. Another way to check you've got the reaction right is the total charge of the reactant species should equal the total charge of the products.